A heat map is a graphical representation of data where the values taken by a variable in a two-dimensional map are represented as colors.Heat maps originated in 2D displays of the values in a data matrix. Larger values were represented by small dark gray or black squares (pixels) and smaller values by lighter squares.

Bioinformatics and Computational Biology Solutions Using R and Bioconductor 第10章的

例子：

Heatmaps, or false color images have a reasonably long history, as has thenotion of rearranging the columns and rows to show structure in the data.They were applied to microarray data by Eisen et al. (1998) and havebecome a standard visualization method for this type of data.A heatmap is a two-dimensional, rectangular, colored grid. It displaysdata that themselves come in the form of a rectangular matrix. The colorof each rectangle is determined by the value of the corresponding entryin the matrix. The rows and columns of the matrix can be rearrangedindependently. Usually they are reordered so that similar rows are placednext to each other, and the same for columns. Among the orderings thatare widely used are those derived from a hierarchical clustering, but manyother orderings are possible. If hierarchical clustering is used, then it iscustomary that the dendrograms are provided as well. In many cases theresulting image has rectangular regions that are relatively homogeneousand hence the graphic can aid in determining which rows (generally thegenes) have similar expression values within which subgroups of samples(generally the columns).The function heatmap is an implementation with many options. In particular,users can control the ordering of rows and columns independentlyfrom each other. They can use row and column labels of their own choosingor select their own color scheme.

The first section of this page uses R to analyse an Acute lymphocytic leukemia (ALL) microarray dataset, producing a heatmap (with dendrograms) of genes differentially expressed between two types of leukemia.

There is a follow on page dealing with how to do this from Python using RPy.

The original citation for the raw data is "Gene expression profile of adult T-cell acute lymphocytic leukemia identifies distinct subsets of patients with different response to therapy and survival" by Chiaretti et al. Blood 2004. (PMID: 14684422)

Alternatively, you can download the package by hand from here or here.

If you are using Windows, download ALL_1.0.2.zip (or similar) and save it. Then from within the R program, use the menu option "Packages", "Install package(s) from local zip files..." and select the ZIP file.

Ignoring the samples which came back negative on this test (NEG), most have been classified as having a translocation between chromosomes 9 and 22 (BCR/ABL), or a translocation between chromosomes 4 and 11 (ALL1/AF4).

For the purposes of this example, we are only interested in these two subgroups, so we will create a filtered version of the dataset using this as a selection criteria:

> eset <- ALL[, ALL$mol.biol %in% c("BCR/ABL", "ALL1/AF4")]

The resulting variable, eset, contains just 47 samples - each with the full 12,625 gene expression levels.

This is far too much data to draw a heatmap with, but we can do one for the first 100 genes as follows:

> heatmap(exprs(eset[1:100,]))

According to the BioConductor paper we are following, the next step in the analysis was to use the lmFit function (from the limma package) to look for genes differentially expressed between the two groups. The fitted model object is further processed by the eBayes function to produce empirical Bayes test statistics for each gene, including moderated t-statistics, p-values and log-odds of differential expression.

The leftmost numbers are row indices, ID is the Affymetrix HGU95av2 accession number, M is the log ratio of expression, A is the log average expression, t the moderated t-statistic, and B is the log odds of differential expression.

Next, we select those genes that have adjusted p-values below 0.05, using a very stringent Holm method to select a small number (165) of genes.

The variable esetSel has data on (only) 165 genes for all 47 samples . We can easily produce a heatmap as follows (in R-2.1.1 this defaults to a yellow/red "heat" colour scheme):

> heatmap(exprs(esetSel))

If you have the topographical colours installed (yellow-green-blue), you can do this:

> heatmap(exprs(esetSel), col=topo.colors(100))

This is getting very close to Gentleman et al.'s Figure 2, except they have added a red/blue banner across the top to really emphasize how the hierarchical clustering has correctly split the data into the two groups (10 and 37 patients).

To do that, we can use the heatmap function's optional argument of ColSideColors. I created a small function to map the eselSet$mol.biol values to red (#FF0000) and blue (#0000FF), which we can apply to each of the molecular biology results to get a matching list of colours for our columns:

One subtle point in the previous examples is that the heatmap function has automatically scaled the colours for each row (i.e. each gene has been individually normalised across patients). This can be disabled using scale="none", which you might want to do if you have already done your own normalisation (or this may not be appropriate for your data):

You might also have noticed in the above snippet, that I have shrunk the row captions which were so big they overlapped each other. The relevant options are cexRow and cexCol.

So far so good - but what if you wanted a key to the colours shown? The heatmap function doesn't offer this, but the good news is that heatmap.2 from the gplots library does. In fact, it offers a lot of other features, many of which I deliberately turn off in the following example:

By default, heatmap.2 will also show a trace on each data point (removed this with trace="none"). If you ask for a key (using key=TRUE) this function will actually give you a combined "color key and histogram", but that can be overridden (with density.info="none").

Don't like the colour scheme? Try using the functions bluered/redblue for a red-white-blue spread, or redgreen/greenred for the red-black-green colour scheme often used with two-colour microarrays:

P.S. If you want to use heatmap.2 from within python using RPy, use the syntax heatmap_2 due to the differences in how R and Python handle full stops and underscores.

What about other microarray data?

Well, I have also documented how you can load NCBI GEO SOFT files into R as a BioConductor expression set object. As long as you can get your data into R as a matrix or data frame, converting it into an exprSet shouldn't be too hard.

Details

If either Rowvor Colvare dendrograms they are honored (and not reordered). Otherwise, dendrograms are computed as dd <- as.dendrogram(hclustfun(distfun(X)))where Xis either xor t(x).

If either is a vector (of “weights”) then the appropriate dendrogram is reordered according to the supplied values subject to the constraints imposed by the dendrogram, by reorder(dd, Rowv), in the row case. If either is missing, as by default, then the ordering of the corresponding dendrogram is by the mean value of the rows/columns, i.e., in the case of rows, Rowv <- rowMeans(x, na.rm=na.rm). If either is NULL, no reordering will be done for the corresponding side.

If scale="row"the rows are scaled to have mean zero and standard deviation one. There is some empirical evidence from genomic plotting that this is useful.

By default four components will be displayed in the plot. At the top left is the color key, top right is the column dendogram, bottom left is the row dendogram, bottom right is the image plot. When RowSideColor or ColSideColor are provided, an additional row or column is inserted in the appropriate location. This layout can be overriden by specifiying appropriate values for lmat, lwid, and lhei. lmatcontrols the relative postition of each element, while lwidcontrols the column width, and lheicontrols the row height. See the help page for layoutfor details on how to use these arguments.

mean and standard deviation of each column: only present if scale="column"

carpet

reordered and scaled 'x' values used generate the main 'carpet'

rowDendrogram

row dendrogram, if present

colDendrogram

column dendrogram, if present

breaks

values used for color break points

col

colors used

vline

center-line value used for column trace, present only if trace="both"or trace="column"

hline

center-line value used for row trace, present only if trace="both"or trace="row"

colorTable

A three-column data frame providing the lower and upper bound and color for each bin

Note

The original rows and columns are reordered in any case to match the dendrogram, e.g., the rows by order.dendrogram(Rowv)where Rowvis the (possibly reorder()ed) row dendrogram.

heatmap.2()uses layoutand draws the imagein the lower right corner of a 2x2 layout. Consequentially, it can not be used in a multi column/row layout, i.e., when par(mfrow= *)or (mfcol= *)has been called.